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Paper   IPM / M / 177
School of Mathematics
  Title:   On eigenvalues of perturbed quadratic matrix polynomials
1.  M. Radjabalipour
2.  A. Salemi
  Status:   Published
  Journal: Integral Equations Operator Theory
  Vol.:  22
  Year:  1995
  Pages:   242-247
  Supported by:  IPM
Among other results, it is shown that if C and K are arbitrary complex n×n matrices and if det(λ02 I+ λ0 C+K)=0 for some λ0 ≠ 0 (resp.  λ0=0), then the Newton diagram of the polynomial t(λ, ϵ)=det (λ2 I+λ(1+ϵ) C+K), expanded in (λ−λ0) and ϵ, has at least a point on or below the line x+y=b ( resp. has no point on or above the line x=y), where b is the algebraic multiplicity of 0 as an eigenvalue of λ02I0 C+K. These are extensions of similar results due to H. Langer, B. Najman, and K. Veseli\acutec proved for diagonable matrices C, and shed light on the eigenvalues of the perturbed quadratic matrix polynomials. Our proofs are independent and seem to be simpler.

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